1. A Dynamic Messenger Problem Jan Fábry University of Economics Prague fabry@vse.cz

2. Structure of presentation _______________________________________________________________________________________ EURO XXII – European Conference on Operations Research, Prague 20072 1.Introduction 2.Static Messenger Problem 3.Messenger Problem with Time Windows 4.Dynamic Messenger Problem 5.Conclusion

3. 1. Introduction _______________________________________________________________________________________ EURO XXII – European Conference on Operations Research, Prague 20073 Messenger problem - example 132 67 89 54 Depot

4. 2. Static Messenger Problem _______________________________________________________________________________________ EURO XXII – European Conference on Operations Research, Prague 20074 Requirements of ALL customers are known before a dispatcher starts to plan the route.

5. 2. Static Messenger Problem _______________________________________________________________________________________ EURO XXII – European Conference on Operations Research, Prague 20075 Model assumptions i i +1 SOURCE (even nodes) DESTINATION (odd nodes) i i +1 NO ! YES

6. 2. Static Messenger Problem _______________________________________________________________________________________ EURO XXII – European Conference on Operations Research, Prague 20076 Traveling Salesman Problem minimize subject to

7. 2. Static Messenger Problem _______________________________________________________________________________________ EURO XXII – European Conference on Operations Research, Prague 20077 Messenger problem - example 1 Depot 132 6 78 9 5 4 Optimal route

8. 3. Messenger Problem with TW _______________________________________________________________________________________ EURO XXII – European Conference on Operations Research, Prague 20078 minimize subject to {Time Window}

9. 4. Dynamic Messenger Problem _______________________________________________________________________________________ EURO XXII – European Conference on Operations Research, Prague 20079 A new requirement for pick-up and delivery can occur during the travel. These two actions will be integrated into the current route.

10. 4. Dynamic Messenger Problem _______________________________________________________________________________________ EURO XXII – European Conference on Operations Research, Prague 200710 Static problem Dynamic problem A new requirement Optimization Re-optimization Heuristic/metaheuristic

11. 4. Dynamic Messenger Problem _______________________________________________________________________________________ EURO XXII – European Conference on Operations Research, Prague 200711 1 Depot 132 6 78 9 5 4 Optimal route10 11  Insertion algorithm

12. 4. Dynamic Messenger Problem _______________________________________________________________________________________ EURO XXII – European Conference on Operations Research, Prague 200712 Insertion algorithm (1) (2)

13. 4. Dynamic Messenger Problem _______________________________________________________________________________________ EURO XXII – European Conference on Operations Research, Prague 200713 Insertion algorithm (1) (2) Extension of the current route

14. 4. Dynamic Messenger Problem _______________________________________________________________________________________ EURO XXII – European Conference on Operations Research, Prague 200714 Re-optimization minimize subject to {Set of non-visited locations} {Index of next location} {Increasing sequence of locations of packages that have not been picked up}

15. 4. Dynamic Messenger Problem _______________________________________________________________________________________ EURO XXII – European Conference on Operations Research, Prague 200715 1 Depot 132 6 78 9 5 4 Optimal route10 11  Re-optimization

16. 5. Conclusion _______________________________________________________________________________________ EURO XXII – European Conference on Operations Research, Prague 200716 Heuristics & metaheuristics Time windows Multiple messengers Capacity - one depot - multiple depots

17. _______________________________________________________________________________________ EURO XXII – European Conference on Operations Research, Prague 200717 Thank you for attention ☺